Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

Abstract

This paper considers a problem of estimating brain effective connectivity from EEG signals using a Granger causality (GC) concept characterized on state-space models. We propose a state-space model for explaining coupled dynamics of the source and EEG signals where EEG is a linear combination of sources according to the characteristics of volume conduction. Our formulation has a sparsity prior on the source output matrix that can further classify active and inactive sources. The scheme is comprised of two main steps: model estimation and model inference to estimate brain connectivity. The model estimation consists of performing a subspace identification and the active source selection based on a group-norm regularized least-squares. The model inference relies on the concept of state-space GC that requires solving a discrete-time Riccati equation for the covariance of estimation error. We verify the performance on simulated data sets that represent realistic human brain activities under several conditions including percentages of active sources, a number of EEG electrodes and the location of active sources. The performance of estimating brain networks is compared with a two-stage approach using source reconstruction algorithms and VAR-based Granger analysis. Our method achieved better performances than the two-stage approach under the assumptions that the true source dynamics are sparse and generated from state-space models. The method is applied to a real EEG SSVEP data set and we found that the temporal lobe played a role of a mediator of connections between temporal and occipital areas, which agreed with findings in previous studies.

Time-Varying Effective Connectivity for Describing the Dynamic Brain Networks of Post-stroke Rehabilitation

“…Therefore, the study of time-varying networks helps us to explore the dynamic process of brain information processing in MI recognition and to capture the time-varying connections of cognitive processes. Including time-varying granger causality analysis (tv-GCA), time-varying partial directed coherence (tv-PDC), and adaptive directed transfer function (ADTF) can get different network connection structures in different cognitive procedures (Li et al, 2015 ; Manomaisaowapak et al, 2015 ). Li et al ( 2016 ) have used an adaptive directed transfer function to construct a time-varying network of P300 and found that different stages of P300 induce different brain network structures.…”